In early beginnings of the past century Felix Hausdorff introduced the concept of a partially ordered set thus extending Richard Dedekind lattice theory which began in the early 1890s. Then the subject lay more or less dormant until Garrett Birkhoff, Oystein Ore and others picked it up in the 1930s. Since then, many noted mathematicians have contributed to the subject, including Garrett Birkhof...

The new learning dynamic of Brown, von Neuman and Nash (1950) is introduced to macroeconomic dynamics via the cobweb model with rational and naive forecasting strategies. This dynamic has appealing properties such as positive correlation and inventiveness. There is persistent heterogeneity in the forecasts and chaotic behavior with bifurcations between periodic orbits and strange attractors for...

In response to [7], we discover the looked for inversion formula for F -nomial coefficients. Before supplying its proof, we generalize F -nomial coefficients to multi F -nomial coefficients and we give their combinatorial interpretation in cobweb posets language, as the number of maximal-disjoint blocks of the form σPk1,k2,...,ks of layer 〈Φ1 → Φn〉. Then we present inversion formula for F -nomi...

This paper generalizes the evolutionary cobweb model with heterogeneous beliefs of Brock and Hommes (1997. Econometrica 65, 1059}1095), to the case of non-linear demand and supply. Agents choose between a simple, freely available prediction strategy such as naive expectations and a sophisticated, costly prediction strategy such as rational expectations, and update their beliefs according to an ...

In response to [6], we discover the looked for inversion formula for F -nomial coefficients. Before supplying its proof, we generalize F -nomial coefficients to multi F -nomial coefficients and we give their combinatorial interpretation in cobweb posets language, as the number of maximal-disjoint blocks of the form σPk1,k2,...,ks of layer 〈Φ1 → Φn〉. Then we present inversion formula for F -nomi...

Sir,?There is an article on the treatment of fever by cobwebs in the Madras Quarterly Journal for April 1863, contributed by Dr. Donaldson, of the Madras Medical Service. He therein states that an article by him had appeared in the Indian Lancet of April 1st, 1861, where probably Mr. Brown noticed it. He usually gave 5 grains of cobweb every three hours, night and day, during both paroxysm and ...

Abstract. The paper investigates how producer’s storage may smoothen, or increase, the endogenous dynamic volatility of commodity markets. A two-season cobweb model is developed for annually harvested crops. This model of intra-year storage has risk averse and naive producers. The model is often periodic but can also be chaotic, i.e., endogenously volatile. The introduction of storage in the mo...

This paper extends the Adaptively Rational Equilibrium Dynamics (ARED) of (Brock and Hommes 1997) by introducing a generalized version of the replicator dynamic of (Sethi and Franke 1995). The Replicator Equilibrium Dynamics (RED) couples the price dynamics of a cobweb model with predictor selection governed by an evolutionary replicator dynamic. We show that the RED supports the main conclusio...

We use least squares support vector machine (LS-SVM) utilizing a binary decision tree for classification of cardiotocogram to determine the fetal state. The parameters of LS-SVM are optimized by particle swarm optimization. The robustness of the method is examined by running 10-fold cross-validation. The performance of the method is evaluated in terms of overall classification accuracy. Additio...

Intrusion Detection System (IDS) is a system, that monitors network traffic and tries to detect suspicious activity. In this paper we discuss the possibilities of application of clustering algorithms and Support Vector Machines (SVM) for use in the IDS. There we used K-means, FarthestFirst and COBWEB algorithms as clustering algorithms and SVM as classification SVM of type 1, known too as C-SVM...